Disk drives write either a +1 or a -1 by orienting the spins of magnetic domain particles on a disk in one direction or the opposite direction. When data is read from the disk, a read head senses the transition of the spins from orientation in a first direction to orientation in a second, opposite direction as a bit boundary peak. The bit boundary peaks of the sensed signal represent the spatial positions where the transitions occur on the disk. The signal sensed by the disk read head is analyzed by a pulse detector circuit to identify the spatial relationship between a bit boundary peak in a first direction and a bit boundary peak in a second direction. The elapsed time represented by the spatial relationship between successive bit boundary peaks indicates how long the digits were written on the disk in one direction or the other, and thus how many 1's and -1's were stored and read.
Noise can obfuscate the location of a peak in a signal. Therefore, the signal from the read head is filtered to band limit the frequencies in the filtered signal and enhance the accuracy of the peak detection. A filter that introduces a pure group delay does not increase the difficulty of extracting spatial information from the filtered signal as the entire signal, and thus relative signal characteristics, are all shifted the same amount of time. However, if the filter introduces a change in the distance between the bit boundary peaks, the spatial relationship between a bit boundary peak in one direction and a bit boundary peak in the opposite direction would be impaired. As a result, it may not be possible to accurately determine how many digits were stored. Thus, the filter must preserve the relative spatial peak-to-peak location by not introducing a phase change.
As disk storage densities increase, magnetic domains become smaller and smaller and bit boundary peaks are packed closer and closer together. When bit boundary peaks are packed closer together, the peaks have a smaller amplitude, and the bit boundary peaks interfere with adjacent peaks, resulting in distorted bit boundary peak positions. The distortion is compensated for through a write predistortion to yield bit boundary peaks during a disk read operation at desired relative locations. The band limiting filter is also used to introduce an increase in magnitude without a change in phase, called boost, to the filtered signal.
A polynomial filter can be synthesized by factoring the polynomial into a product of terms, typically quadratic, with each quadratic term implemented in cascade. The cascade implementation is functionally equivalent to multiplication in the frequency domain or a convolution in the time domain.
A biquadratic filter has typically been used to introduce boost. The term biquadratic identifies that there is a quadratic expression in both the numerator and denominator of the mathematical expression defining the filter. A biquadratic filter has been used because poles and zeros occur in pairs, and quadratic terms are readily implemented to realize a filter. Designing higher order filters by using a cascade of successive biquadratic filter sections is well known.
A filter implemented using transconductance cells is shown in J. M. Khoury's "Design of a 15-MHz CMOS-time Filter with On-chip Tuning," IEEE Journal of Solid State Circuits, Dec. 19, 1991, Vol. 26, No. 12, pp. 1988-1997. Transconductance cells can also be used to realize a biquadratic filter.
A traditional method to provide boost in a biquadratic filter uses the generalized biquadratic structure shown as prior art in FIG. 3. This structure is shown by Geiger, R. L. and Sanchez-Sinencio, E., IEEE Circuits and Devices Magazine, Mar. 19, 1985, pp. 20-32, at p. 28. The output voltage V.sub.o is described by the following equation: ##EQU1##
To eliminate the first order term in the numerator so as to have a quadratic term factorable into two complex conjugate roots, V.sub.B is set to zero. Boost is achieved by making input V.sub.C proportional to the negative of input V.sub.A, and then controlling the level of input V.sub.A. The lower plate of capacitor C.sub.2 is driven by a voltage source, V.sub.C, that is proportional to input V.sub.A.
Another known method to introduce boost in a disk drive filter is to take the higher order frequency domain equation of a disk drive filter and factor the equation into lower order terms. Each of the second order numerator terms factors into two terms from which two roots are identified. Each of the two roots is placed in a different biquadratic section of the filter. Mathematically, the same results are achievable as with the FIG. 3 circuit. A problem with this design is that the gains that must be established to define the numerator roots (zeros) are independent. For the phase of the two roots to cancel, the positions of the roots must be maintained at mirror image locations across the imaginary axis in the frequency domain. Since the gain achieved in the two biquadratic sections will approximate the gains necessary to precisely locate the zeros at mirror image locations, but in practice will not be exact, the phase delay introduced by each zero in the passband of the filter will not cancel. A net phase shift will be introduced, along with an incorrect amplitude, resulting in both an amplitude distortion and nonuniform group delay which are not characteristics of the desired boost.
It is desired to have a filter introduce boost into a signal passing therethrough such that the contribution of the filter zeros to the phase shift in the filter passband cancel. In this manner, the filter zeroes introduce only the desired amplitude increase known as boost. It is further desired for the boost setting to be independent of the filter pole frequencies, such that variations in the boost setting does not change the pole frequencies of the filter and scaling in the pole frequencies does not change the boost setting.